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3 On geometric inverse problems and microlocal analysis
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Mikko Salo
Abstract
This work gives an expository account of certain applications of microlocal analysis in three geometric inverse problems. We will discuss the geodesic X-ray transform inverse problem, the Gelfand problem for the wave equation on a Riemannian manifold and the Calderón problem for the Laplace equation on a Riemannian manifold.
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Abstract
This work gives an expository account of certain applications of microlocal analysis in three geometric inverse problems. We will discuss the geodesic X-ray transform inverse problem, the Gelfand problem for the wave equation on a Riemannian manifold and the Calderón problem for the Laplace equation on a Riemannian manifold.
You are currently not able to access this content.
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- 1 Generalized Radon transforms 1
- 2 Nonstandard Sobolev scales and the mapping properties of the X-ray transform on manifolds with strictly convex boundary 35
- 3 On geometric inverse problems and microlocal analysis 77
- 4 Inverse problems in cosmological X-ray tomography 139
- 5 The weighted X-ray transform and applications 167
- Index 187
Chapters in this book
- Frontmatter I
- Preface V
- Contents VII
- 1 Generalized Radon transforms 1
- 2 Nonstandard Sobolev scales and the mapping properties of the X-ray transform on manifolds with strictly convex boundary 35
- 3 On geometric inverse problems and microlocal analysis 77
- 4 Inverse problems in cosmological X-ray tomography 139
- 5 The weighted X-ray transform and applications 167
- Index 187
